That looks fine. Its definitely a long tentacle plate or Heliofungia
Mysis are small shrimp. You can buy them frozen in blister packs
Make sure food lands on it, food either naturally drifts to it or you can use a turkey baster to gently squirt food onto it.

Plate coral one of the most difficult to keep in marine tanks. Pet shops should be banned from stocking them..

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I havent witnessed this before. My three have all been bulletproof. One used to spend most of the time covered in substrate.
They can sometimes take a while to get used to light/flow of a new tank so initial placement can be crucial to their survival